Reply to "There is no 690 GeV resonance"

TL;DR

Consoli et al. address a critique of their proposal for a second Higgs-like resonance near $M_H^{\rm theor} = 690\,(30)$ GeV alongside the 125 GeV Higgs. They argue that a two-mass structure arises naturally in the Gaussian Effective Action, with $m_h^2 \sim M_H^2 L^{-1}$ and $M_H$ tied to the electroweak scale via $M_H = K v$ with $K \approx 2.81$, supported by lattice scalar-propagator studies. They defend the treatment of the propagator via $G^{-1}(p) = p^2 + M_H^2 A(p,M_H)$ and emphasize that a single, perturbative one-loop picture does not capture the full two-scale dynamics, while the explicit form of $A(p,M_H)$ and the distinction between momentum regimes clarify the interpretation. The results predict a consistent high-mass resonance around $690$ GeV and suggest potential experimental signatures in collider data, with the two-mass scenario persisting in the cutoff theory and being corroborated by lattice simulations.

Abstract

In a recent note [1], J. M. Cline criticised our idea that, besides the known Higgs boson with mass $m_h=$ 125 GeV, the Higgs field $\cal H$ could exhibit a relatively narrow, second resonance with theoretical mass $(M_H)^{\rm Theor} = 690\,(30)$ GeV. His criticism addresses both the basic theory part as well as our phenomenological analysis, in which we show that the characteristic, experimental signature of the proposed new resonance may already be visible in various LHC data. As for the comparison with experiment, Cline altogether ignores our most recent article [2], except for its title, and limits himself to just show an old plot from a preprint from five years ago. For this reason, as far as the phenomenology is concerned, there is nothing to reply to. Instead, we will briefly reply to his criticism on the theoretical part. Our conclusion is that Cline has completely ignored basic aspects of our work.